Entropy of an analytic signal

Journal of Russian Laser Research

Volumn 27, Issue 5, 2006, Pages 405-413

  Man'ko, Margarita A ^a  

^a LEBEDEV PHYSICAL INSTITUTE   (Russian Federation)

Author keywords

Analytic signal; Integral transform; Radon transform; Shannon entropy; Tomography

Indexed keywords

EID: 33748926960     PISSN: 10712836     EISSN: 15738760     Source Type: Journal    
DOI: 10.1007/s10946-006-0023-y     Document Type: Conference Paper

References (40)

1. J. B. J. Fourier, Théorie Analytique de la Chaleur, in: G. Darbous (ed.), Oeuvres de Fourier, Gauthiers-Villars, Paris (1888), Tome premier.
2. K. B. Howell, "Fourier transforms," in: A. D. Poularikas (ed.), The Transforms and Applications Handbook, CRC Press & IEEE Press, Boca Raton, Florida (1996), p. 95.
3. L. Cohen, Proc. IEEE, 77, 941 (1989).
4. L. Cohen, IEEE Trans. Signal Process., 44, 1080 (1996).
5. M. A. Man'ko, J. Russ. Laser Res., 21, 411 (2000).
6. J. Ville, "Théorie et applications de la notion de signal analytique," Cables et Transmission, 2, 61 (1948).
7. E. Wigner, Phys. Rev., 40, 749 (1932).
8. A. D. Poularikas (ed.), The Transforms and Applications Handbook, CRC Press & IEEE Press, Boca Raton, Florida (1996).
9. J. Radon, "Über die Bestimmung von Funktionen durch ihre Integralwerte längs gewisser Mannigfaltigkeiten", Berichte Sachsische Akademie der Wissenschaften, Leipzig, Mathematische-Physikalische Klasse, 69 (1917), S. 262.
10. V. I. Man'ko and R. V. Mendes, Phys. Lett. A, 263, 53 (1999); "Noncommutative time-frequency tomography of analytic signals," SISSA-LANL E-print Physics/9712022 Data Analysis, Statistics, and Probability.
11. M. A. Man'ko, J. Russ. Laser Res., 20, 226 (1999).
12. M. A. Man'ko, "Optical tomography approach in signal analysis," SISSA-LANL E-print quant-ph/9906010; in: D. Han, Y. S. Kim, and S. Solimeno (eds.), Sixth International Conference on Squeezed States and Uncertainty Relations (Naples, Italy, May 1999), NASA Conference Proceedings in CD 2000-209899, Goddard Space Flight Center, Greenbelt, Maryland (1999).
13. M. A. Man'ko, "Fractional Fourier analysis and quantum propagators," in: H.-D. Doebner, V. K. Dobrev, J.-D. Hennig, and W. Luecke (eds.), Proceedings of the International Symposium 'Quantum Theory and Symmetries' (Goslar, Germany, July 1999), World Scientific, Singapore (2000), p. 226.
14. M. A. Man'ko, "Quantum-tomography method in information processing and fractional Fourier transform," in: A. N. Sisakyan, G. S. Pogosyan, and L. G. Mardoyan (eds.), XXIII International Colloquium on Group Theoretical Methods in Physics (Dubna, Russia, July-August 2000), Joint Institute for Nuclear Research Press, Dubna, Moscow Region, Russia (2000), p. 640.
15. G. M. D'Ariano, S. Mancini, V.I. Man'ko, and P. Tombesi, Quantum Semiclass. Opt., 8, 1017 (1996).
16. M. A. Man'ko, V. I. Man'ko, and R. V. Mendes, J. Phys. A: Math. Gen., 34, 8321 (2001).
17. M. A. Man'ko, J. Russ. Laser Res., 22, 505 (2001).
18. M. A. Man'ko, "Wavelets and transforms in information processing," in: E. Kapuścik and A. Horzela (eds.), Proceedings of the Second International Symposium on Quantum Theory and Symmetries (Krakow, Poland, July 2001), World Scientific, Singapore (2002), p. 473.
19. M. A. Man'ko, "Unified view of tomographic and other transforms in signal analysis," in: J. P. Gaseau, R. Kerner, J.-P. Antoine, S. Métens, and J.-Y. Thibon (eds.), Group 24: Physical and Mathematical Aspects of Synnetries. Proceedings of the 24th International Colloquium on Group Theoretical Methods in Physics (Paris, July 2002), Institute of Physics Publishers, Bristol, Conference Series Number 173, p. 887.
20. S. Mancini, V. I. Man'ko, and P. Tombesi, Phys. Lett. A, 213, 1 (1996).
21. S. Mancini, V. I. Man'ko, and P. Tombesi, Found. Phys., 27, 801 (1997).
22. Olga Man'ko and V. I. Man'ko, J. Russ. Laser Res., 18, 407 (1997).
23. M. A. Man'ko, J. Russ. Laser Res., 22, 168 (2001).
24. M. A. Man'ko, "Quantum-tomography method in information processing," in: P. Tombesi and O. Hirota (eds.), Quantum Communication, Computing, and Measurements 3. Proceedings of the Fifth International Conference on Quantum Communication, Measurements and Computing (Capri, Italy, July 2000), Kluwer Academic/Plenum Publishers, New York (2002), p. 147.
25. S. De Nicola, R. Fedele, M. A. Man'ko, and V. I. Man'ko, Eur. Phys. J. B, 36, 385 (2003).
26. S. De Nicola, R. Fedele, M. A. Man'ko, and V. I. Man'ko, "Wigner picture and tornographic representation of envelope solitons," in: M. Ablowitz, M. Boiti, F. Pempinelli, and B. Prinari (eds.), Proceedings of International Workshop 'Nonlinear Physics: Theory and Experiment. IP (Gallipoli, Lecce, Italy, June-July 2002), World Scientific, Singapore (2003), p. 372.
27. M. A. Man'ko, "Soliton signals in tomographic representation," in H. Moya-Cessa, R. Jauregui, S. Hacyan, and O. Castaños (eds.), Proceedings of the 8th International Conference on Squeezed States and Uncertainty Relations (Puebla, Mexico, June 2003), Rinton (2004), p. 246.
28. M. A. Man'ko, S. De Nicola, R. Fedele, and V. I. Man'ko, "Symplectic group and solitons in BEC as probability distributions corresponding to nonlinear signals," in: G. S. Pogosyan, L. E. Vicent, and K.-B. Wolf (eds.), Group Theoretical Methods in Physics, Proceedings of the XXV International Colloquium on Group Theoretical Methods in Physics (Cocoyoc, Mexico, 2-6 August 2004), Institute of Physics Publishers, Bristol (2005), Conference Series Number 185, p. 385.
29. S. De Nicola, R. Fedele, M. A. Man'ko, and V. I. Man'ko, J. Russ. Laser Res., 25, 1 (2004).
30. E. P. Gross, Nuovo Cimento, 20, 454 (1961).
31. L. P. Pitaevskii, Sov. Phys. JETP, 13, 451 (1961).
32. C. E. Shannon, Bell Syst. Tech. J., 27, 379 (1948).
33. V. V. Dodonov and V. I. Man'ko, Invariants and Evolution of Nonstationary Quantum Systems, Proceedings of the P. N. Lebedev Physical Institute, Nauka, Moscow (1987), Vol. 183 [Nova Science, Commack, New York (1989)].
34. S. De Nicola, R. Fedele, M. A. Man'ko, and V. I. Man'ko, "New uncertainty relation for tomographic entropy: Application to squeezed states and solitons," ArXiv quant-ph/0607200 v1; Eur. Phys. J. B (2006, in press).
35. J. Bertrand and P. Bertrand, Found. Phys., 17, 397 (1987).
36. K. Vogel and H. Risken, Phys. Rev. A, 40, 2847 (1989).
37. M. A. Man'ko, J. Russ. Laser Res., 23, 433 (2002).
38. J. S. Bell, Physica, 1, 195 (1964).
39. J. S. Bell, Speakable and Unspeakable in Quantum Mechanics, Cambridge University Press, Cambridge (1987).
40. S. Mancini, V. I. Man'ko, E. V. Shchukin, and P. Tombesi, J. Opt. B: Quantum Semiclass. Opt., 5, S333 (2003).